Numerical methods for evolution hemivariational inequalities. (English) Zbl 1319.49010
Han, Weimin (ed.) et al., Advances in variational and hemivariational inequalities. Theory, numerical analysis, and applications. Cham: Springer (ISBN 978-3-319-14489-4/hbk; 978-3-319-14490-0/ebook). Advances in Mechanics and Mathematics 33, 111-144 (2015).
Summary: We consider numerical methods of solving evolution subdifferential inclusions of nonmonotone type. In the main part of the chapter we apply the Rothe method for a class of second order problems. The method consists in constructing a sequence of piecewise constant and piecewise linear functions being a solution of an approximate problem. Our main result provides a weak convergence of a subsequence to a solution of the exact problem. Under some more restrictive assumptions we obtain also uniqueness of the exact solution and a strong convergence result. Next, for the reference class of problems we apply a semidiscrete Faedo-Galerkin method as well as a fully discrete one. For both methods we present a result on optimal error estimates.
For the entire collection see [Zbl 1309.49002].
For the entire collection see [Zbl 1309.49002].
MSC:
| 49J40 | Variational inequalities |
| 65K15 | Numerical methods for variational inequalities and related problems |
| 49J52 | Nonsmooth analysis |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 47J22 | Variational and other types of inclusions |
| 35L85 | Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators |
